To train our neural networks, we generate the data set containing \(552,000\)  training inputs \(\left\lbrace \vec{x}_{i}\right\rbrace \)  and \(552,000\)  corresponding labels \(\left\lbrace {y}_{i}\right\rbrace \)  using the numerical method in Refs. [1]}, [2]}. Each \(\vec{x}_{i} \in \left\lbrace \vec{x}_{i}\right\rbrace \)  represents a vector of 29 variables, and label \({y}_{i}\)  represents the corresponding key rate. There are 16 variables in each \(\vec{x}_{i}\)  that are the right parts of the first four restrictions of Eq. (REF ), 12 variables in each \(\vec{x}_{i}\)  are non-diagonal elements of the right side matrix of the fifth restriction of Eq. (REF ), and the remaining variable is excess noise \(\xi \) . The 29 variables in each \(\vec{x}_i\)  can be calculated in the experiment by using experimental parameters and experimental observations. In our simulation, These random training inputs \(\left\lbrace \vec{x}_{i}\right\rbrace \)  are generated directly from seven experimental parameters (transmission distance \(L\) , light intensity \(\mu \) , excess noise \(\xi \) , and probability \(p0\) , \(p1\) , \(p2\)  and \(p3\) ) and the following method.
